To solve the equation
[tex]\[
-\frac{1}{2} n^2 + 18 = 0,
\][/tex]
we need to isolate [tex]\( n \)[/tex].
1. Start by moving the constant term to the other side of the equation:
[tex]\[
-\frac{1}{2} n^2 = -18.
\][/tex]
2. Next, to eliminate the fraction, multiply both sides of the equation by [tex]\(-2\)[/tex]:
[tex]\[
n^2 = 36.
\][/tex]
3. To solve for [tex]\( n \)[/tex], take the square root of both sides:
[tex]\[
n = \pm \sqrt{36}.
\][/tex]
4. This gives us:
[tex]\[
n = \pm 6.
\][/tex]
So, the solution of this equation is:
[tex]\[
n = \pm 6.
\][/tex]
